College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.1 - Inverse Functions - 4.1 Exercises: 45

Answer

$f$ and $g$ are inverses of each other

Work Step by Step

The two functions are inverses if $(f\circ g)(x)=x$ and if $(g\circ f)(x)=x$ First, $f(g(x))=\frac{\frac{2x+1}{x-1}+1}{\frac{2x+1}{x-1}-2}$. After multiplying both the nominator and the denominator by (x-1), we get: $\frac{2x+1+x-1}{2x+1-2x+2}=\frac{3x}{3}=x$. Second, $g(f(x))=\frac{2\frac{x+1}{x-2}+1}{\frac{x+1}{x-2}-1}$. After both the numerator and the denominator by $x-2$, we get $\frac{2x+2+x-2}{x+1-x+2}=\frac{3x}{3}=x$ Therefore, $f$ and $g$ are inverses of each other.
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